Identifying conditions and traits that allow an introduced species to grow and spread, from being initially rare to becoming abundant (defined as invasiveness), is the crux of invasion ecology. Invasiveness and abundance are related but not the same, and we need to differentiate these concepts. Predicting both species abundance and invasiveness and their relationship in an invaded community is highly contextual, being contingent on the community trait profile and its invasibility. We operationalised a three-pronged invasion framework that considers traits, environmental context, and propagule pressure. Specifically, we measure the invasiveness of an alien species by combining three components (performance reflecting environmental suitability, product of species richness and the covariance between interaction strength and species abundance, and community-level interaction pressure); the expected population growth rate of alien species simply reflects the total effect of propagule pressure and the product of their population size and invasiveness. The invasibility of a community reflects the size of opportunity niches (the integral of positive invasiveness in the trait space) under the given abiotic conditions of the environment. Both species abundance and the surface of invasiveness over the trait space can be dynamic and variable. Whether an introduced species with functional traits similar to those of an abundant species in the community exhibits high or low invasiveness depends largely on the kernel functions of performance and interaction strength with respect to traits and environmental conditions. Knowledge of the covariance between interaction strength and species abundance and these kernel functions, thus, holds the key to accurate prediction of invasion dynamics.

Biodiversity Informatics Unit African Institute for Mathematical Sciences Muizenberg South Africa

Centre for Invasion Biology Department of Botany and Zoology Stellenbosch University Stellenbosch South Africa

Centre for Invasion Biology Department of Mathematical Sciences Stellenbosch University Stellenbosch South Africa

Department of Ecology Charles University Prague Czech Republic

Institute of Botany Czech Academy of Sciences Prague Czech Republic

National Institute for Theoretical and Computational Sciences Stellenbosch University Stellenbosch South Africa

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